A. Flores-Franulic

A Jensen type inequality for fuzzy integrals

In this paper, we show a Jensen type inequality for the Sugeno integral. We also discuss some conditions assuring the satisfaction of opposite inequality (reverse Jensen inequality).

A Chebyshev type inequality for fuzzy integrals

Abstract In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that: ⨍ 0 1 fg d μ ⩾ ⨍ 0 1 f d μ ⨍ 0 1 g d μ , where μ is the Lebesgue measure on R and f , g : [ 0 , 1 ] → [ 0 , ∞ ) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented.

A convolution type inequality for fuzzy integrals

In this paper we show a Bushell–Okrasinski type inequality for fuzzy integrals. More precisely, we show that: s⨍01(1-t)s-1g(t)sdt⩾⨍01g(t)dts, where g:[0,1]→[0,∞) is a continuous and strictly decreasing function and s ⩾ 2.

A Hardy-type inequality for fuzzy integrals

Abstract In this paper, we prove a Hardy-type inequality for fuzzy integrals. More precisely, we show that ⨍ 0 1 f p ( x ) d x 1 p + 1 ⩾ ⨍ 0 1 F x p d x , where p ⩾ 1 , f : [ 0 , 1 ] → [ 0 , ∞ ) is an integrable function and F ( x ) = ⨍ 0 x f ( t ) d t . An analogous inequality is also obtained on the interval [ 0 , ∞ ) .

Markov type inequalities for fuzzy integrals

In this paper, we study some fuzzy Markov type inequalities and its connections with some fundamental properties of the Sugeno integral.

On the level-continuity of fuzzy integrals

In this paper we define the level-convergence of measurable functions on a fuzzy measure space, by using the closure operator in the Moore sense. We study some of the properties of this convergence and give conditions for the continuity of the fuzzy integral in relation to the level-convergence.

General Barnes-Godunova-Levin type inequalities for Sugeno integral

Integral inequalities play important roles in classical probability and measure theory. Non-additive measure is a generalization of additive probability measure. Sugenos integral is a useful tool in several theoretical and applied statistics which has been built on non-additive measure. For instance, in decision theory, the Sugeno integral is a median, which is indeed a qualitative counterpart to the averaging operation underlying expected utility. In this paper, Barnes-Godunova-Levin type inequalities for the Sugeno integral on abstract spaces are studied in a rather general form and, for this, we introduce some new technics for the treatment of concave functions in the Sugeno integration context. Also, several examples are given to illustrate the validity of this inequality. Moreover, a strengthened version of Barnes-Godunova-Levin type inequality for Sugeno integrals on a real interval based on a binary operation * is presented.

Stability of fixed points set of fuzzy contractions

Abstract In this paper, we define the fuzzy fixed points set of a fuzzy contraction mapping, we study some properties, and we prove a stability result in relation to the uniform convergence.

Ostrowski type inequalities for interval-valued functions using generalized Hukuhara derivative

The present paper is devoted to obtaining some Ostrowski type inequalities for interval-valued functions. In this context we use the generalized Hukuhara derivative for interval-valued functions. Also some examples and consequences are presented. Mathematical subject classification: Primary: 26E25; Secondary: 35A23.

Fatou's lemma for Sugeno integral

Abstract Fatou’s lemma plays an important role in classical probability and measure theory. Non-additive measure is a generalization of additive probability measure. Sugeno’s integral is a useful tool in several theoretical and applied statistics which have been built on non-additive measure. In this paper, a Fatou-type lemma for Sugeno integral is shown. The studied inequality is based on the classical Fatou lemma for Lebesgue integral. To illustrate the proposed inequalities some examples are given.